Spin-1/2 frustrated antiferromagnet on a spatially anisotopic square lattice: contribution of exact diagonalizations

Abstract

The phase diagram of a spin-1/2 $J-J^{\prime }-J_2$ model is investigated by means of exact diagonalizations on finite samples. This model is a generalization of the $J_1-J_2$ model on the square lattice with two different nearest-neighbor couplings $J,J^{\prime }$ and may be also viewed as an array of coupled Heisenberg chains. The results suggest that the resonnating valence bond state predicted by Nersesyan and Tsvelik [Phys. Rev. B {\bf 67}, 024422 (2003)] for $J_2=0.5J^{\prime }\ll J$ is realized and extends beyond the limit of small interchain coupling along a curve nearly coincident with the line where the energy per spin is maximum. This line is likely bordered on both side by a columnar dimer long range order. This columnar order could extends for $J^{\prime }\to J$ which correspond to the $J_1-J_2$ model.

14 pages, 21 figures, final version

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